oscillatory singular integrals
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2019 ◽  
Vol 31 (2) ◽  
pp. 535-542
Author(s):  
Yibiao Pan

AbstractA sharp logarithmic bound is established for the {H^{1}}-norm of oscillatory singular integrals with quadratic phases and Hölder class kernels. Prior results had relied on a {C^{1}}-assumption on the kernel.


2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Hussain Al-Qassem ◽  
Leslie Cheng ◽  
Yibiao Pan

We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature.


2017 ◽  
Vol 238 (2) ◽  
pp. 121-132
Author(s):  
Hussain Al-Qassem ◽  
Leslie Cheng ◽  
Yibiao Pan

2017 ◽  
Vol 4 (1) ◽  
pp. 1314066
Author(s):  
M.K. Hota ◽  
A.K. Saha ◽  
P. Ojha ◽  
P.K. Mohanty ◽  
J. Alberto Conejero

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